Boult has been battling a side strain, which forced him to miss New Zealand’s Second Test against England but has travelled with the squad to Western Australia.
The Black Caps appear cautious in their management of Boult with a tight schedule for the Second and Third Tests at the MCG and SCG in late December and early January.
Boult has taken 16 wickets in two day-night Test matches and will be a key figure for the pink ball Test at Perth’s Optus Stadium if available.
“We’ll have another look at (Trent) today, before deciding anything tomorrow,” Williamson told the media on Wednesday.
“We’ll look at it in the long-term for the whole series. He’s tracking nicely and looked good yesterday. There’s a number of factors in that decision.”
Williamson confirmed Ross Taylor was fine after copping a knock to his thumb in nets, while he said Colin de Grandhomme, who missed the Second Test against England with an abdominal tear, was “tracking nicely”.
The New Zealand captain admitted quick Lockie Ferguson was being considered for his Test debut amid calls to draft him into the XI.
Williamson added that his second-ranked side expected a tough challenge against Australia, with limited time for adjustment after their series against England.
“Australia are always really tough opposition to face,” Williamson said. “In their own backyard they’re very very clinical as we’ve seen over a long time.
“It’s been a fairly quick turnaround from the England series at home but it’s very important we look to make the adjustments quickly.”